Solve for $x$ and $y$ using elimination. ${x-2y = -3}$ ${-4x-5y = -66}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${4x-8y = -12}$ $-4x-5y = -66$ Add the top and bottom equations together. $-13y = -78$ $\dfrac{-13y}{{-13}} = \dfrac{-78}{{-13}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x-2y = -3}\thinspace$ to find $x$ ${x - 2}{(6)}{= -3}$ $x-12 = -3$ $x-12{+12} = -3{+12}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {-4x-5y = -66}\thinspace$ and get the same answer for $x$ : ${-4x - 5}{(6)}{= -66}$ ${x = 9}$